Inkscape x o is the canonical vector drawing application. If you wish to create diagram like flowcharts, charts, etc. then Dia x o may be more appropriate.
The GIMP x o is a popular bitmap graphics programme that competes with PhotoShop. If you work in a demanding domain, say film, you will want to investigate CinePaint x o. It's a 32-bit paint program that was forked from GIMP code. It has "been used on many feature films, including The Last Samurai where it was used to add flying arrows." I have yet to try this out, since it seems too much for my modest needs. Looks fantastic, however!
A further bitmap programme is PhotoFiltre w, which is free for private use, noncommercial or educational use. It is optimised for image retouching, but I haven't spent much time coming to terms with it. The forum is in French and documentation is minimal.
I don't do any video or animation work, but have used Wax w, a flexible video compositing and special effects package.
When it comes to utilities I sing the praises of ColorCop w, a brilliant eyeglass / magnifier and pixel colour grabber, essential for matching colours in graphics, screen shot manipulation, and so on.
Exifer w helps you manage the metadata (EXIF/IPTC) of digital camera pix. It's postcardware. Exif Image Viewer w lists EXIF photo information, presenting thumbnails and histograms.
IrfanView w is predominantly an image viewer, but I find it invaluable for two tasks: converting images to icon format and grabbing screen captures.
Last, but not least, I must encourage you to spend money on one single product. Noise Ninja is an almost magical tool which removes noise from images, particularly those from digital cameras. The cheapest version is $35, and will make you think your camera is far more expensive than it really is!
If you think I've saved you hundreds of [insert your monetary unit here] then make a donation using the PayPal link. Thanks!
o Open Source
w win32 only